I have a house that is painted white with green shutters. There is a wood walkway to get to my house and there is wood in my yard to block the wood chips from spreading. I also have some plants in the yard.

I am looking for a nice but neutral color in the green, beige, brown, or maybe grey family, preferably from Benjamin Moore or Behr. It currently is painted a light blue but it simply does not go well.

Welcome Home100:
The wood could be painted green to blend in with the grass, or to make it really outstanding, it could be painted red. The red would look good for the remainder of the year at least, Christmas colors.
I painted my new deck grey with white railings. Use a porch and floor enamel for more durability.
Glenn

Interesting color system you have. Blue on that wood sounds bad. Red would make your home and yard look like an Italian flag (white house, green shutters, red yard wood). What color green is on the shutters? that is a key issue. I'd go with a sage green--a shade of muted gray-green on the yard wood. It'd probably look even better with the shutters in the same color sage green or one shade darker or lighter.

Walmart carries Dutchboy paint which is as good as Behr but a lot cheaper, they have an Exterior Extreme Adhesion paint that works great and even paints vinyl siding.
The "greens" are heading out of style and the browns are coming back in, a nice taupe/medium brown for the house and a light mushroom shade for the trim and maybe match the roof shingles color to the shutters and garage door if there is one
Don't use gloss or semi gloss , it is too much shine, you can use the satin or the flat as they both hold up the same now

Tried to remove this as I thought we were talkjing about painting the whole house not the flower bed wood